Maximum principles and overdetermined problems for Hessian equations
In this article we investigate some Hessian type equations. Our main aim is to derive new maximum principles for some suitable P-functions, in the sense of L.E. Payne, that is for some appropriate functional combinations of u(x) and its derivatives, where u(x) is a solution of the given Hessian type...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | , |
| Format: | article |
| Published: |
2021
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/11073/25083 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1864513440281788416 |
|---|---|
| author | Enache, Cristian |
| author2 | Marras, Monica Porru, Giovanni |
| author2_role | author author |
| author_facet | Enache, Cristian Marras, Monica Porru, Giovanni |
| author_role | author |
| dc.creator.none.fl_str_mv | Enache, Cristian Marras, Monica Porru, Giovanni |
| dc.date.none.fl_str_mv | 2021 2022-11-30T07:28:40Z 2022-11-30T07:28:40Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | Enache, C.; Marras, M.; Porru, G. Maximum principles and overdetermined problems for Hessian equations. (2021) Advances in Pure and Applied Mathematics, Issue 3, https://doi.org/10.21494/ISTE.OP.2021.0701 1867-1152 http://hdl.handle.net/11073/25083 10.21494/ISTE.OP.2021.0701 |
| dc.language.none.fl_str_mv | en_US |
| dc.publisher.none.fl_str_mv | ISTE Group |
| dc.relation.none.fl_str_mv | https://doi.org/10.21494/ISTE.OP.2021.0701 |
| dc.subject.none.fl_str_mv | Monge-Ampere equations Hessian Equations Maximum principles Overdetermined problems |
| dc.title.none.fl_str_mv | Maximum principles and overdetermined problems for Hessian equations |
| dc.type.none.fl_str_mv | Peer-Reviewed Published version info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | In this article we investigate some Hessian type equations. Our main aim is to derive new maximum principles for some suitable P-functions, in the sense of L.E. Payne, that is for some appropriate functional combinations of u(x) and its derivatives, where u(x) is a solution of the given Hessian type equations. To find the most suitable P-functions, we first investigate the special case of a ball, where the solution of our Hessian equations is radial, since this case gives good hints on the best functional to be considered later, for general domains. Next, we construct some elliptic inequalities for the well-chosen P-functions and make use of the classical maximum principles to get our new maximum principles. Finally, we consider some overdetermined problems and show that they have solutions when the underlying domain has a certain shape (spherical or ellipsoidal). |
| format | article |
| id | aus_9234d23ab30001e6c9790fa5973f5f6d |
| identifier_str_mv | Enache, C.; Marras, M.; Porru, G. Maximum principles and overdetermined problems for Hessian equations. (2021) Advances in Pure and Applied Mathematics, Issue 3, https://doi.org/10.21494/ISTE.OP.2021.0701 1867-1152 10.21494/ISTE.OP.2021.0701 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/25083 |
| publishDate | 2021 |
| publisher.none.fl_str_mv | ISTE Group |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Maximum principles and overdetermined problems for Hessian equationsEnache, CristianMarras, MonicaPorru, GiovanniMonge-Ampere equationsHessian EquationsMaximum principlesOverdetermined problemsIn this article we investigate some Hessian type equations. Our main aim is to derive new maximum principles for some suitable P-functions, in the sense of L.E. Payne, that is for some appropriate functional combinations of u(x) and its derivatives, where u(x) is a solution of the given Hessian type equations. To find the most suitable P-functions, we first investigate the special case of a ball, where the solution of our Hessian equations is radial, since this case gives good hints on the best functional to be considered later, for general domains. Next, we construct some elliptic inequalities for the well-chosen P-functions and make use of the classical maximum principles to get our new maximum principles. Finally, we consider some overdetermined problems and show that they have solutions when the underlying domain has a certain shape (spherical or ellipsoidal).American University of SharjahISTE Group2022-11-30T07:28:40Z2022-11-30T07:28:40Z2021Peer-ReviewedPublished versioninfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfEnache, C.; Marras, M.; Porru, G. Maximum principles and overdetermined problems for Hessian equations. (2021) Advances in Pure and Applied Mathematics, Issue 3, https://doi.org/10.21494/ISTE.OP.2021.07011867-1152http://hdl.handle.net/11073/2508310.21494/ISTE.OP.2021.0701en_UShttps://doi.org/10.21494/ISTE.OP.2021.0701oai:repository.aus.edu:11073/250832024-08-22T12:01:34Z |
| spellingShingle | Maximum principles and overdetermined problems for Hessian equations Enache, Cristian Monge-Ampere equations Hessian Equations Maximum principles Overdetermined problems |
| status_str | publishedVersion |
| title | Maximum principles and overdetermined problems for Hessian equations |
| title_full | Maximum principles and overdetermined problems for Hessian equations |
| title_fullStr | Maximum principles and overdetermined problems for Hessian equations |
| title_full_unstemmed | Maximum principles and overdetermined problems for Hessian equations |
| title_short | Maximum principles and overdetermined problems for Hessian equations |
| title_sort | Maximum principles and overdetermined problems for Hessian equations |
| topic | Monge-Ampere equations Hessian Equations Maximum principles Overdetermined problems |
| url | http://hdl.handle.net/11073/25083 |